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Erschienen in: Quality & Quantity 2/2017

08.10.2016

A diagram to detect serial dependencies: an application to transport time series

verfasst von: Luca Bagnato, Lucio De Capitani, Antonio Punzo

Erschienen in: Quality & Quantity | Ausgabe 2/2017

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Abstract

The Ljung–Box test is typically used to test serial independence even if, by construction, it is generally powerful only in presence of pairwise linear dependence between lagged variables. To overcome this problem, Bagnato et al. recently proposed a simple statistic defining a serial independence test which, differently from the Ljung–Box test, is powerful also under a linear/nonlinear dependent process characterized by pairwise independence. The authors also introduced a normalized bar diagram, based on p-values from the proposed test, to investigate serial dependence. This paper proposes a balanced normalization of such a diagram taking advantage of the concept of reproducibility probability. This permits to study the strength and the stability of the evidence about the presence of the dependence under investigation. An illustrative example based on an artificial time series, as well as an application to a transport time series, are considered to appreciate the usefulness of the proposal.

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Literatur
Zurück zum Zitat Anderson, H.M., Vahid, F.: Nonlinear correlograms and partial autocorrelograms. Oxford Bull. Econ. Stat. 67, 957–982 (2005)CrossRef Anderson, H.M., Vahid, F.: Nonlinear correlograms and partial autocorrelograms. Oxford Bull. Econ. Stat. 67, 957–982 (2005)CrossRef
Zurück zum Zitat Bagnato, L., Punzo, A.: On the use of χ2-test to check serial independence. Stat. Appl. VIII(1), 57–74 (2010) Bagnato, L., Punzo, A.: On the use of χ2-test to check serial independence. Stat. Appl. VIII(1), 57–74 (2010)
Zurück zum Zitat Bagnato, L., Punzo, A., Nicolis, O.: The autodependogram: a graphical device to investigate serial dependences. J. Time Ser. Anal. 33(2), 233–254 (2012)CrossRef Bagnato, L., Punzo, A., Nicolis, O.: The autodependogram: a graphical device to investigate serial dependences. J. Time Ser. Anal. 33(2), 233–254 (2012)CrossRef
Zurück zum Zitat Bagnato, L., De Capitani, L., Punzo, A.: Detecting serial dependencies with the reproducibility probability autodependogram. Adv. Stat. Anal. 98(1), 35–61 (2014a)CrossRef Bagnato, L., De Capitani, L., Punzo, A.: Detecting serial dependencies with the reproducibility probability autodependogram. Adv. Stat. Anal. 98(1), 35–61 (2014a)CrossRef
Zurück zum Zitat Bagnato, L., De Capitani, L., Punzo, A.: Testing serial independence via density-based measures of divergence. Method. Comput. Appl. Probab. 16(3), 627–641 (2014b)CrossRef Bagnato, L., De Capitani, L., Punzo, A.: Testing serial independence via density-based measures of divergence. Method. Comput. Appl. Probab. 16(3), 627–641 (2014b)CrossRef
Zurück zum Zitat Bagnato, L., De Capitani, L., Mazza, A., Punzo, A.: SDD: an R package for serial dependence diagrams. J. Stat. Softw. 64(Code Snippet 2):1–19 (2015) Bagnato, L., De Capitani, L., Mazza, A., Punzo, A.: SDD: an R package for serial dependence diagrams. J. Stat. Softw. 64(Code Snippet 2):1–19 (2015)
Zurück zum Zitat Bagnato, L., De Capitani, L., Punzo, A.: The Kullback–Leibler autodependogram. J. Appl. Stat. 43(14), 2574–2594 (2016a)CrossRef Bagnato, L., De Capitani, L., Punzo, A.: The Kullback–Leibler autodependogram. J. Appl. Stat. 43(14), 2574–2594 (2016a)CrossRef
Zurück zum Zitat Bagnato, L., De Capitani, L., Punzo, A.: Testing for serial independence: beyond the Portmanteau approach. Am. Stat. (accepted) (2016b) Bagnato, L., De Capitani, L., Punzo, A.: Testing for serial independence: beyond the Portmanteau approach. Am. Stat. (accepted) (2016b)
Zurück zum Zitat Box, G.E.P., Tiao, G.C.: Intervention analysis with applications to economic and environmental problems. J. Am. Stat. Assoc. 70(349), 70–79 (1975)CrossRef Box, G.E.P., Tiao, G.C.: Intervention analysis with applications to economic and environmental problems. J. Am. Stat. Assoc. 70(349), 70–79 (1975)CrossRef
Zurück zum Zitat Cochran, W.G.: Some methods for strengthening the common \(\chi ^2\) tests. Biometrics 10(4), 417–451 (1954)CrossRef Cochran, W.G.: Some methods for strengthening the common \(\chi ^2\) tests. Biometrics 10(4), 417–451 (1954)CrossRef
Zurück zum Zitat Cryer, J.D., Chan, K.S.: Time Series Analysis: With Applications in R. Springer Texts in Statistics. Springer, New York (2010) Cryer, J.D., Chan, K.S.: Time Series Analysis: With Applications in R. Springer Texts in Statistics. Springer, New York (2010)
Zurück zum Zitat De Capitani, L.: An introduction to RP-testing. Epidemiol. Biostat. Public Health 10(1) (2013) De Capitani, L.: An introduction to RP-testing. Epidemiol. Biostat. Public Health 10(1) (2013)
Zurück zum Zitat De Capitani, L., De Martini, D.: On stochastic orderings of the Wilcoxon rank sum test statisticwith applications to reproducibility probability estimation testing. Stat. Probab. Lett. 81(8), 937–946 (2011)CrossRef De Capitani, L., De Martini, D.: On stochastic orderings of the Wilcoxon rank sum test statisticwith applications to reproducibility probability estimation testing. Stat. Probab. Lett. 81(8), 937–946 (2011)CrossRef
Zurück zum Zitat De Capitani, L., De Martini, D.: Reproducibility probability estimation and testing for the Wilcoxon rank-sum test. J. Stat. Comput. Simul. 85(3), 468–493 (2015)CrossRef De Capitani, L., De Martini, D.: Reproducibility probability estimation and testing for the Wilcoxon rank-sum test. J. Stat. Comput. Simul. 85(3), 468–493 (2015)CrossRef
Zurück zum Zitat De Capitani, L., De Martini, D.: Reproducibility probability estimation and RP-testing for some nonparametric tests. Entropy 18(4), 142 (2016)CrossRef De Capitani, L., De Martini, D.: Reproducibility probability estimation and RP-testing for some nonparametric tests. Entropy 18(4), 142 (2016)CrossRef
Zurück zum Zitat De Martini, D.: Reproducibility probability estimation for testing statistical hypotheses. Stat. Probab. Lett. 78(9), 1056–1061 (2008)CrossRef De Martini, D.: Reproducibility probability estimation for testing statistical hypotheses. Stat. Probab. Lett. 78(9), 1056–1061 (2008)CrossRef
Zurück zum Zitat Diks, C.: Nonparametric Tests for Independence. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 6252–6271. Springer, New York (2009)CrossRef Diks, C.: Nonparametric Tests for Independence. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 6252–6271. Springer, New York (2009)CrossRef
Zurück zum Zitat Genest, C., Rémillard, B.: Test of independence and randomness based on the empirical copula process. Test 13(2), 335–369 (2004)CrossRef Genest, C., Rémillard, B.: Test of independence and randomness based on the empirical copula process. Test 13(2), 335–369 (2004)CrossRef
Zurück zum Zitat Goodman, S.N.: A comment on replication, \(p\)-values and evidence. Stat. Med. 11(7), 875–879 (1992)CrossRef Goodman, S.N.: A comment on replication, \(p\)-values and evidence. Stat. Med. 11(7), 875–879 (1992)CrossRef
Zurück zum Zitat Hall, P., Wolff, R.: On the strength of dependence of a time series generated by a chaotic map. J. Time Ser. Anal. 16(6), 571–583 (1995)CrossRef Hall, P., Wolff, R.: On the strength of dependence of a time series generated by a chaotic map. J. Time Ser. Anal. 16(6), 571–583 (1995)CrossRef
Zurück zum Zitat Hallin, M., Mélard, G.: Rank-based tests for randomness against first-order serial dependence. J. Am. Stat. Assoc. 83(404), 1117–1128 (1988)CrossRef Hallin, M., Mélard, G.: Rank-based tests for randomness against first-order serial dependence. J. Am. Stat. Assoc. 83(404), 1117–1128 (1988)CrossRef
Zurück zum Zitat Johnson, N., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, vol. 2. Wiley, New York (1995) Johnson, N., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, vol. 2. Wiley, New York (1995)
Zurück zum Zitat King, M.: Testing for autocorrelation in linear regression models: a survey. In: King, M.L., Giles, D.E.A. (eds.) Specification Analysis in the Linear Model, pp. 19–73. Routledge Kegan & Paul, London (1987) King, M.: Testing for autocorrelation in linear regression models: a survey. In: King, M.L., Giles, D.E.A. (eds.) Specification Analysis in the Linear Model, pp. 19–73. Routledge Kegan & Paul, London (1987)
Zurück zum Zitat Lehmann, E.L.: Testing Statistical Hypotheses. Springer, New York (1997) Lehmann, E.L.: Testing Statistical Hypotheses. Springer, New York (1997)
Zurück zum Zitat Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65(2), 297–303 (1978)CrossRef Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65(2), 297–303 (1978)CrossRef
Zurück zum Zitat Zhou, Z.: Measuring nonlinear dependence in time-series, a distance correlation approach. J. Time Ser. Anal. 33(3), 438–457 (2012)CrossRef Zhou, Z.: Measuring nonlinear dependence in time-series, a distance correlation approach. J. Time Ser. Anal. 33(3), 438–457 (2012)CrossRef
Metadaten
Titel
A diagram to detect serial dependencies: an application to transport time series
verfasst von
Luca Bagnato
Lucio De Capitani
Antonio Punzo
Publikationsdatum
08.10.2016
Verlag
Springer Netherlands
Erschienen in
Quality & Quantity / Ausgabe 2/2017
Print ISSN: 0033-5177
Elektronische ISSN: 1573-7845
DOI
https://doi.org/10.1007/s11135-016-0426-y

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